Learning diverse policies for non-prehensile manipulation is essential for improving skill transfer and generalization to out-of-distribution scenarios. In this work, we enhance exploration through a two-fold approach within a hybrid framework that tackles both discrete and continuous action spaces. First, we model the continuous motion parameter policy as a diffusion model, and second, we incorporate this into a maximum entropy reinforcement learning framework that unifies both the discrete and continuous components. The discrete action space, such as contact point selection, is optimized through Q-value function maximization, while the continuous part is guided by a diffusion-based policy. This hybrid approach leads to a principled objective, where the maximum entropy term is derived as a lower bound using structured variational inference. We propose the Hybrid Diffusion Policy algorithm (HyDo) and evaluate its performance on both simulation and zero-shot sim2real tasks. Our results show that HyDo encourages more diverse behavior policies, leading to significantly improved success rates across tasks - for example, increasing from 53% to 72% on a real-world 6D pose alignment task. Project page: https://leh2rng.github.io/hydo

Current literature, aiming to surpass the "Chain-of-Thought" approach, often resorts to an external modus operandi involving halting, modifying, and then resuming the generation process to boost Large Language Models' (LLMs) reasoning capacities. This mode escalates the number of query requests, leading to increased costs, memory, and computational overheads. Addressing this, we propose the Algorithm of Thoughts -- a novel strategy that propels LLMs through algorithmic reasoning pathways, pioneering a new mode of in-context learning. By employing algorithmic examples, we exploit the innate recurrence dynamics of LLMs, expanding their idea exploration with merely one or a few queries. Our technique outperforms earlier single-query methods and stands on par with a recent multi-query strategy that employs an extensive tree search algorithm. Intriguingly, our results suggest that instructing an LLM using an algorithm can lead to performance surpassing that of the algorithm itself, hinting at LLM's inherent ability to weave its intuition into optimized searches. We probe into the underpinnings of our method's efficacy and its nuances in application.